Field of the Invention
This invention relates to manipulation of audio signals, and more particularly to method and apparatus for changing the timbre, tuning and/or intonation of audio signals.
When two ordinary musical notes are played together they define an interval between them corresponding to the difference between their scale tones. A musical interval is generally considered to be consonant if it sounds pleasant or restful; a consonant interval has little or no musical tension. Dissonance is the degree to which an interval sounds unpleasant or rough; dissonant intervals generally sound tense and unresolved. Certain musical intervals are widely perceived as consonant (for instance the notes C and G on a piano) while other intervals are perceived as dissonant (for instance, the notes C and C sharp on a piano). Intervals are usually expressed in terms of scale tones between the notes in question, and the characteristic dissonance or consonance of an interval is generally independant of the absolute pitches of the notes. Thus, the half-tone interval C-C sharp is conventionally considered to be equivalent to the half-tone interval G-G sharp despite the shift in absolute pitch. Stated in musical jargon, intervals can be transposed without losing their characteristic dissonance or consonance. Intervals can be identified in several different ways. For example, the interval C-G can be described as the interval of a fifth (i.e., five tones of a major scale based on the lower note, C), or as an interval of seven semitones (based on a standard, tempered, 12-tone scale), or as a freqency ratio of about 1:1.5.
Dissonance may also be perceived among groups of notes. Thus, when a performer plays or sings out of tune with an accompanying orchestra, or when an instrument has not been properly tuned, the result is quickly perceived as being dissonant.
As part of the study of the perception of musical sounds, the physical attributes of accoustical phenomenon have been taken into consideration. For example, it has long been recognized that sound phenomena travel through the air in waves, and musical sounds are generally characterized as having the wave attributes of frequency and amplitude. The frequency attribute is generally associated with the pitch of the sound, i.e., whether the note is high or low, whereas the amplitude is associated with loudness.
In studying the perception of consonance and dissonance, Plomp et al, as reported in the article "Tonal Consonance and Critical Bandwidth", 38 JASA, 548-560 (1965), asked a number of volunteers to rate the dissonance or consonance of a pair of "pure" tones, i.e., tones having wave forms corresponding to sine waves. The two tones were played together, and one was kept at a constant reference frequency while the frequency of the other was slowly changed. The results of the study are set forth in FIG. 1, which shows that as the interval between the two tones increased, the dissonance between them was first perceived to increase, and then to decrease. Contrary to conventional belief regarding ordinary tones, the interval at which maximum dissonance was perceived for the pure tones, sometimes referred to herein as the "critical interval", was different for different reference frequencies, as indicated by the various curves in the graph of FIG. 1. For example, when the reference, i.e., unison, frequency was 125 Hz, the critical interval was about four semitones; whereas at a reference frequency of 2000 Hz, the critical interval was about one semitone. Generally, the higher the reference frequency, the smaller the critical interval and the more quickly dissonance dissipated as the interval between the tones increased beyond the critical interval.